Bjørn Olav Hogstad

A MIMO Mobile-To-Mobile Channel Model: Part I - The Reference Model

In this paper, we propose a multiple-input multiple-output (MIMO) channel model for mobile-to-mobile communications. This so-called MIMO mobile-to-mobile channel model is derived from the geometrical two-ring scattering model under the assumption that both the transmitter and the receiver are moving. In Part I of our paper, we focus on the reference model, which is based on the assumption that the transmitter and the receiver are surrounded by an infinite number of local scatterers. From a wave model, the complex channel gains are derived and their statistical properties are studied. General analytical solutions are provided for the three-dimensional (3-D) space-time cross-correlation function (CCF). We show that this 3-D function can be expressed as the product of two 2-D space-time CCFs, which are introduced as the transmit and receive CCF. Especially for the latter CCFs, closed-form expressions and numerical results are presented in case of isotropic scattering. The procedure presented in our paper provides an important framework for designers of future mobile-to-mobile communication systems to verify new transmission concepts under certain propagation conditions

Two new sum-of-sinusoids-based methods for the efficient generation of multiple uncorrelated rayleigh fading waveforms

This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the deterministic sum-of-sinusoids (SOS) channel modeling principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting deterministic SOS-based channel simulator fulfills all main requirements imposed by the reference model with given correlation properties derived under two-dimensional isotropic scattering conditions. The proposed methods are useful for the design of simulation models for diversity-combined Rayleigh fading channels, relay fading channels, frequency-selective channels, and multiple-input multiple-output (MIMO) channels.

A Wideband MIMO Channel Model Derived From the Geometric Elliptical Scattering Model

In this paper, we present a reference model for a wideband multiple-input multiple-output (MIMO) channel based on the geometric elliptical scattering model. The model takes into account the exact relationship between the angle of departure (AOD) and the angle of arrival (AOA). Based on this relationship, the statistical properties of the reference model are studied. Analytical solutions are presented for the three- dimensional (3D) space-time cross-correlation function (CCF), the temporal autocorrelation function (ACF), the 2D space CCF, and finally the frequency correlation function (FCF). The correlation properties are studied and visualized under the assumption of isotropic as well as non-isotropic scattering conditions. The proposed reference model can be used as a starting point for the derivation of a frequency-selective space-time MIMO channel simulator enabling the performance evaluation of multi-antenna wideband communication systems. The reference model is also quite useful for studying the MIMO channel capacity under various propagation conditions imposed by the geometry of the underlying scattering model.

A Mimo Mobile-To-Mobile Channel Model: Part II - The Simulation Model

In this paper, we propose a multiple-input multiple-output (IMIMO) mobile-to-mobile channel simulation model derived from a non-realizable reference model presented in Part I of our paper. The underlying reference model is based on the geometrical two-ring scattering model, where both the transmitter and the receiver are moving. A closed-form solution is provided for the three dimensional (3-D) space-time cross-correlation function (CCF) of the simulation model. An important result is that this CCF is ergodic. Also, our results show that this 3-D function can be expressed as a product of two 2-D space-time CCF, called the transmit and the receive CCF. It is shown that the parameters of the simulation model can be determined for any given space-time CCF describing the reference model. In case of isotropic scattering, we present a closed-form solution of the model parameters and illustrate some numerical results for the transmit and receive CCF. Finally, simulation results show an excellent correspondence between the statistical and time average of the MIMO channel capacity. This supports the hypothesis that the MIMO capacity is ergodic with respect to the mean

Exact Closed-Form Expressions for the Distribution, Level-Crossing Rate, and Average Duration of Fades of the Capacity of MIMO Channels

This paper deals with some important statistical properties of the multiple-input multiple-output (MIMO) channel capacity. We assume that all the subchannels are uncorrelated. In case of single-input multiple-output (SIMO) and multiple-input single-output (MISO) channels, exact closed-form expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity. Furthermore, these exact closed-form expressions are extended to characterize the statistical properties of the maximum MIMO channel capacity. The correctness of the derived closed-form expressions is confirmed by simulations.

A space-time channel simulator for MIMO channels based on the geometrical one-ring scattering model

This paper introduces a general concept for the design of efficient multi-input multi-output (MIMO) narrowband fading channel simulators. The proposed procedure is applied on a reference model for the geometrical one-ring scattering model consisting of an infinite number of local scatterers lying on a ring around the mobile station (MS). The statistical properties of both the reference model and the simulation model are studied. Closed-form solutions are presented, e.g., for the space-time cross-correlation function (CCF), the time autocorrelation function (ACF), and the two-dimensional (2D) space CCF. It is shown how the parameters of the MIMO channel simulator can be determined for any given space-time CCF describing the reference model. The excellent performance of the proposed space-time channel simulator is demonstrated by comparing its temporal and spatial correlation properties with those of the reference model. Moreover, it is demonstrated how the channel simulator can be used to analyse the capacity of MIMO channels from time-domain simulations.

Two New Methods for the Generation of Multiple Uncorrelated Rayleigh Fading Waveforms

This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the sum-of-sinusoids principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting sum-of-sinusoids-based channel simulator fulfills all main requirements imposed by the reference model with given correlation properties derived under two-dimensional isotropic scattering conditions. The proposed methods are useful for the design of simulation models for diversity-combined Rayleigh fading channels, frequency-selective channels, and multiple-input multiple-output (MIMO) channels

A New Design Concept for High-Performance Fading Channel Simulators Using Set Partitioning

In this paper, we introduce a new technique for the design of high-performance Rayleigh fading channel simulators. The proposed design method uses set partitioning – a technique, which plays a key role in the design of trellis-coded modulation schemes. We show how set partitioning can be used to design multiple uncorrelated fading waveforms enabling the simulation of Rayleigh fading channels. For the important case of isotropic scattering, we show that the sample average of the generated waveforms results in a deterministic process, the autocorrelation function (ACF) of which tends to the zeroth-order Bessel function of the first kind as the number of sample functions increases. The proposed procedure is completely deterministic. The comparison with a stochastic procedure using Monte Carlo techniques will be made. A study of the performance shows clearly that the new technique using set partitioning outperforms by far existing Monte Carlo methods.

A Wideband Space-Time MIMO Channel Simulator Based on the Geometrical One-Ring Model

In this paper, we extend the geometrical one-ring multi-input multi-output (MIMO) channel model with respect to frequency-selectivity. Our approach enables the design of efficient and accurate simulation models for wideband space-time MIMO channels under isotropic scattering conditions. Two methods will be provided to compute the parameters of the simulation model. Especially, the space, time, and frequency correlation properties of the proposed wideband space-time MIMO channel simulator are studied analytically. It is shown that any given discrete or continuous power delay profile (PDP) can be incorporated in the simulation model. The high accuracy of the simulation model is demonstrated by comparing its statistical properties with those of the underlying reference model. Our procedure provides an important framework for developers of future wideband mobile communication systems to test and to verify new high data rate transmission concepts employing, e.g., space-time coded MIMO orthogonal frequency division multiplexing (OFDM) techniques.

Exact Closed-Form Expressions for the Distribution, the Level-Crossing Rate, and the Average Duration of Fades of the Capacity of OSTBC-MIMO Channels

This paper deals with some important statistical properties of the channel capacity of multiple-input-multiple-output (MIMO) systems with orthogonal space-time block code (OSTBC) transmission. We assume that all the subchannels are uncorrelated. For OSTBC-MIMO systems, exact closed-form expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity. Furthermore, it will be shown that these exact closed-form expressions can be used to characterize the channel capacity of single-input-multiple-output (SIMO) and multiple-input-single-output (MISO) systems. In addition, a Gaussian approximation to the exact LCR of the capacity of OSTBC-MIMO systems is derived. The correctness of the derived closed-form expressions and the approximation is confirmed by simulations.